Multi-dimensional NMR spectra are generally quite complex. This constitutes a problem in the analysis of the structure of organic or inorganic compounds, wherein larger molecules have more complex multi-dimensional NMR spectra. The data acquisition of spectra with acceptable resolution and the interpretation of such spectra is therefore very difficult.
Standard NMR methods are e.g. the HSQC (Heteronuclear Single Quantum Coherence) or HMBC (Heteronuclear Multiple Bond Correlation), see IUPAC recommendations for NMR pulse sequences (Angew. Chem. 2003, 115, 3293-3301). Reynolds and Enriquez describe (J. Nat. Prod. 2002, 65, 221-244) NMR methods for analyzing the structure of natural substances. Frydman (WO 2004/011899) describes a method for acquiring multi-dimensional NMR spectra with one single scan, wherein partitions of a sample are subdivided into a set of independent parts of different resonance frequency ranges, and the sample is measured slice by slice (in dependence on the volume) with selective pulses (thereby simultaneously applying strong gradient pulses). Disadvantageously, this method is insensitive and relatively large sample amounts or high substance concentrations are required. It is also disadvantageous in that it is difficult to carry out, since the signals from the different scans must be added and the requirements for reproducibility of the gradient field strengths are high. K. Takasugi describes a method for spectral reconstruction of convoluted NMR spectra on the basis of multiple convolution, wherein all excited frequencies undergo the same convolution in the indirect dimension during data acquisition, which corresponds to frequency-independent folding (46th ENC Conference, Apr. 10 to 15, 2005, Providence, R.I., USA; Abstract online available on Apr. 6, 2005).
Dunn and Sidebottom (Magn. Reson. Chem. 2005, 43, 124-131) describe a method for calculating back folded NMR spectra with the aim to accelerate data acquisition and the evaluation of the structural confirmation of small organic molecules, wherein 2 or 3 NMR spectra are measured during data acquisition with different reduced spectral windows in the indirect dimension.
Two-dimensional (2D), I,S-correlation experiments consist of a sequence of radio frequency pulses and delays which effect transfer of magnetization between the spins I and S. The chemical shifts of the S-nuclei are acquired in an indirect (digitized) evolution time t1. The delay, during which the evolution of chemical shifts of the S-nuclei takes place, is thereby incremented in steps. This results in modulation of the NMR signal with the frequencies of the S-nuclei during t1. After the magnetization transfer, the chemical shift of the I-nuclei during t2 is directly detected. Fourier transformation along both time axes produces a 2D spectrum with the chemical shifts of the S and I spins as axes. This concept can be easily extended by introducing additional indirect time domains to more than two dimensions (M. Sattler in Angew. Chem. 2004, 116, 800-804). A two-dimensional NMR experiment consists of several phases, the first so-called preparation phase, a second so-called evolution and mixing phase, and the actual detection phase in which an interferogram (FID) is recorded. The time of the evolution phase, which is called t1, is a variable waiting time within a millisecond to second range, within which chemical shift and spin-spin couplings develop. The evolution and mixing phase is followed by time t2, which is also constant. The data recorded in a two-dimensional NMR experiment is often shown in a so-called contour diagram. Such a contour diagram shows a section along a contour line through the cross signals of the spectrum. These two-dimensional experiments can also be performed as part of multi-dimensional experiments.
The standard method for acquiring data of a multi-dimensional NMR spectrum is based on the application of a certain sequence and succession of excitation pulses of high frequency (pulses) and waiting times (delays). The coherence orders of magnetization thereby generated, their transfer to other coherences, and the rules for selecting the desired magnetizations are entirely described by the product operator formalism.
NMR experiments, during which the frequencies were not convoluted in the indirection evolution phases, are synonymously called “normal NMR experiments”, “conventional NMR experiments” or “standard-NMR experiments” below. Conventional multi-dimensional NMR spectra are e.g. homonuclear and heteronuclear multi-dimensional NMR experiments, such as HSQC (J. Am. Chem. Soc. 1992, 114, 10663-10665), HMBC, COSY, TOCSY, HSQC-TOCSY, in particular, 2 and 3-dimensional NMR experiments. The dimension of multi-dimensional NMR experiments, e.g. of two-dimensional heteronuclear NMR experiments, is the dimension of the chemical shift of the protons and the dimension of the chemical shift of the observed heteronuclei, e.g. the carbon atoms.
In the conventional method for data acquisition of a multi-dimensional NMR spectrum, the evolution time is usually linearly incremented in the evolution phase, wherein the incrementation time Δt1 in the evolution phase meets the Nyquist theorem (equation 1) in order to provide the correct spectral window in the indirect dimension.IN0=1/(Nd0×BF1×SW1), wherein  Equation 1                d0=initial delay (initial waiting time)        Nd0=number of Δt1 increments        SW1=spectral window in the indirect dimension        BF1=basic frequency (e.g. at 9.39 T for 1H 400.13 Hz and for 13C 100.58 Hz),        IN0=incrementation time        
Realization of the above-described experimental conditions thereby observing the Nyquist theorem for correct digitization of the frequencies yields the cross signals in the frequency domain after Fourier transformation (FT) in both dimensions (equation 2), wherein the chemical shift of the measured cross signals are correctly represented in the indirect dimension, i.e. are not folded.S(t1,t2)→FT→S(ν1,ν2), wherein  Equation 2                S(t1,t2)=signal after incrementation time        S(ν1,ν2)=Fourier-transformed signals        
Equation 1 shows that the indirect spectral window SW1 is inversely proportional to the incrementation time IN0 (=Δt1). In consequence thereof, the indirect spectral window SW1 is reduced when Δt1 is extended, and consequently, the frequencies of those cross signals of a multi-dimensional NMR spectrum, which are outside of the selected spectral window, are no longer correctly digitized and thus do not occur at the original chemical shift in the NMR spectrum. This phenomenon of folding in the data acquisition of NMR spectra is extensively described in the literature (two-dimensional NMR spectroscopy, 2nd ed. 1994, W. R. Croasmun and R. M. K. Carlson, Wiley-VCH, pages 493-503) and generally reduces the overall measuring time and increases the digital resolution of the cross signals, which results from equations 3-5:DR=SW [Hz]/TD1*, wherein  Equation 3                SW[Hz]=spectral window in Hertz        DR=digital resolution,        TD1*=complex number of experimentsDR=1/AQ(t1)  Equation 4        AQ(t1)=acquisition time in the indirect dimension according to equation 5.AQ(t1)=Nd0×IN0×TD1*  Equation 5        
For the chemical shifts (called “frequencies” or “apparent frequency” νi in this context) of the cross signals in the indirect dimension of all excited coherences in the evolution time and irrespective of a possible violation of the Nyquist theorem, there is a direct functional dependence on the Δt1 incrementation time in accordance with equation 6.νi(Ωs)=f(Δt1)νi+1(Ωs)=f(Δt1), wherein Equation 6                νi(Ωs), νi+1(Ωs)=chemical shift of the cross peak i or i+1,        f(Δt1)=function of the incrementation time Δt1.        
Analysis of the cross signals (cross peaks) of a multi-dimensional NMR spectrum, e.g. a HSQC spectrum, shows, upon closer observation of the resonance frequencies, that the cross signals arrange themselves in preferably overlying signal groups (peak cluster) in frequency space in dependence on their chemical shift. In consequence thereof, there are frequency ranges in the multi-dimensional NMR spectrum, which generally contain no cross signals and therefore no information.
This observation is substantiated by the fact that the aromatic protons with few electrons (low field-shifted signal areas) in first approximation always result in cross signals with carbons in low field shifted areas in an HSQC-NMR spectrum. Since, however, routine measurements are performed over the entire desired chemical shift range in order to satisfy the Nyquist theorem, there are compulsorily void frequency spaces which contain only a few signals or none at all. A conventional HSQC spectrum of an organic molecule of a molecular mass of between 300 and 500 g/mol usually yields an NMR spectrum in which more than 95% of the frequency areas contain no information in the form of cross signals. For small molecules, it is estimated that up to 99% of the frequency space is not utilized.
In NMR spectroscopy, there are moreover different types of radio frequency pulses, so-called RF pulses. The “hard pulses” are rectangular pulses with wide excitation bandwidth (rectangular high power pulses with a wide frequency excitation band). The “hard pulses” are non-selective. “Shape pulses” are pulses which selectively excite defined frequency ranges. Such pulses are e.g. Gauss, rectangular, sine, BURP pulses and are collectively called shaped pulses or selective pulses below (amplitude and power shaped pulses with a selective excitation band), see e.g. Freeman, Journal of Progress in Nuclear Magnetic Resonance Spectroscopy 1998, 32, 59-106.